Statistical Tests Overview

Here is the good news: the MCAT will never ask you to calculate a t-test statistic, run an ANOVA, or perform a chi-square test by hand. But it will absolutely show you a research passage and ask which test the researchers should have used - or whether the test they chose was appropriate. Think of it like knowing which tool to grab from a toolbox without needing to build the tool yourself.

The Decision: What Kind of Data Do You Have?

Choosing the right statistical test comes down to two questions:

1. What type of data is the outcome? Continuous (numbers on a scale, like blood pressure) or categorical (groups, like “survived” vs. “died”)?
2. How many groups are being compared?

T-Test: Comparing Means of Two Groups

Use a t-test when you are comparing the average (mean) of a continuous variable between exactly two groups.

Examples:

• Does Drug A lower blood pressure more than placebo? (Drug group mean vs. placebo group mean)
• Do men and women differ in average resting heart rate?
• Is there a difference in exam scores before vs. after a tutoring program? (paired t-test)

There are two main variants:

• Independent t-test: Two separate groups (e.g., treatment vs. control).
• Paired t-test: The same group measured twice (e.g., before and after treatment).

ANOVA: Comparing Means of Three or More Groups

ANOVA (Analysis of Variance) extends the logic of the t-test to three or more groups. Instead of asking “do these two groups differ?” it asks “do any of these groups differ from any other?”

Examples:

• Comparing average recovery time across three treatment protocols.
• Testing whether four different diets produce different weight loss.
• Comparing exam scores across five study methods.

ANOVA produces a single p-value that tells you whether at least one group differs from the others. It does not tell you which specific groups differ - that requires follow-up tests (post hoc tests).

Chi-Square Test: Comparing Frequencies (Categorical Data)

Use a chi-square test when both your variables are categorical and you are comparing observed frequencies to expected frequencies.

Examples:

• Does the ratio of blood types in a sample differ from the expected population ratio?
• Is there an association between smoking status (yes/no) and lung cancer (yes/no)?
• Does a coin-flip experiment match the expected $\frac{50}{50}$ distribution?

Chi-square is the test to use when your data is counts in categories, not measurements on a continuous scale.

Correlation and Regression: Relationships Between Continuous Variables

When you want to measure the relationship between two continuous variables (not compare groups), use correlation or regression.

• Correlation gives you the r value: the strength and direction of the linear relationship.
• Linear regression gives you the equation of the best-fit line (y = mx + b), allowing prediction. It tells you how much y changes for each unit change in x.

Examples:

• What is the relationship between study hours and exam scores?
• Does increasing drug dose predict blood pressure reduction?
• Is there a linear relationship between age and reaction time?

The Decision Table